R Code 1 : Bayes Rule Example #2

Consider the dreaded disease Dipsidoodleitis. There are actually two forms of the disease, Type I and Type II, with the later being more severe. Dipsidoodleitis is detected by a blood test. Values for people without dipsidoodleitis are normally distributed, M=70, sd=10. Values for people with Type I and Type II are distributed with M=80, sd=14 and M=110, sd=20, respectively. If a patient has a value of 90, what are the probabilities that she is dipsidoodleitis free, has the Type I version, or has the Type II version.